# SpaceToBatch¶

Versioned name : SpaceToBatch-2

Category : Data movement

Short description : The SpaceToBatch operation divides “spatial” dimensions [1, ..., N - 1] of the data input into a grid of blocks of shape block_shape, and interleaves these blocks with the batch dimension (0) such that in the output, the spatial dimensions [1, ..., N - 1] correspond to the position within the grid, and the batch dimension combines both the position within a spatial block and the original batch position. Prior to division into blocks, the spatial dimensions of the input are optionally zero padded according to pads_begin and pads_end.

Detailed description :

The operation is equivalent to the following transformation of the input tensor data of shape [batch, D_1, D_2 ... D_{N - 1}] and block_shape, pads_begin, pads_end of shapes [N] to Y output tensor.

Zero-pad the start and end of dimensions $$[D_0, \dots, D_{N - 1}]$$ of the input according to pads_begin and pads_end :

$x = [batch + P_0, D_1 + P_1, D_2 + P_2, \dots, D_{N - 1} + P_{N - 1}]$
$x' = reshape(x, [batch, \frac{D_1 + P_1}{B_1}, B_1, \frac{D_2 + P_2}{B_2}, B_2, \dots, \frac{D_{N - 1} + P_{N - 1}}{B_{N - 1}}, B_{N - 1}])$
$x'' = transpose(x', [2, 4, \dots, (N - 1) + (N - 1), 0, 1, 3, \dots, N + (N - 1)])$
$y = reshape(x'', [batch \times B_1 \times \dots \times B_{N - 1}, \frac{D_1 + P_1}{B_1}, \frac{D_2 + P_2}{B_2}, \dots, \frac{D_{N - 1} + P_{N - 1}}{B_{N - 1}}]$

where

• $$P_i$$ = pads_begin[i] + pads_end[i]

• $$B_i$$ = block_shape[i]

• $$P_0$$ for batch dimension is expected to be 0 (no-padding)

• $$B_0$$ for batch is ignored

Attributes

No attributes available.


Inputs

• 1 : data - input N-D tensor [batch, D_1, D_2 ... D_{N - 1}] of T1 type with rank >= 2. Required.

• 2 : block_shape - input 1-D tensor of T2 type with shape [N] that is equal to the size of data input shape. All values must be >= 1. block_shape[0] is expected to be 1. Required.

• 3 : pads_begin - input 1-D tensor of T2 type with shape [N] that is equal to the size of data input shape. All values must be non-negative. pads_begin specifies the padding for the beginning along each axis of data input . It is required that block_shape[i] divides data_shape[i] + pads_begin[i] + pads_end[i]. pads_begin[0] is expected to be 0. Required.

• 4 : pads_end - input 1-D tensor of T2 type with shape [N] that is equal to the size of data input shape. All values must be non-negative. pads_end specifies the padding for the ending along each axis of data input. It is required that block_shape[i] divides data_shape[i] + pads_begin[i] + pads_end[i]. pads_end[0] is expected to be 0. Required.

Outputs

• 1 : N-D tensor with shape [batch \* block_shape[0] \* block_shape[1] \* ... \* block_shape[N - 1], (D_1 + pads_begin[1] + pads_end[1]) / block_shape[1], (D_2 + pads_begin[2] + pads_end[2]) / block_shape[2], ..., (D_{N -1} + pads_begin[N - 1] + pads_end[N - 1]) / block_shape[N - 1] of the same type as data input.

Types

• T1 : any supported type.

• T2 : any supported integer type.

Example

<layer type="SpaceToBatch" ...>
<input>
<port id="0">       <!-- data -->
<dim>2</dim>    <!-- batch -->
<dim>6</dim>    <!-- spatial dimension 1 -->
<dim>10</dim>   <!-- spatial dimension 2 -->
<dim>3</dim>    <!-- spatial dimension 3 -->
<dim>3</dim>    <!-- spatial dimension 4 -->
</port>
<port id="1">       <!-- block_shape value: [1, 2, 4, 3, 1] -->
<dim>5</dim>
</port>
<port id="2">       <!-- pads_begin value: [0, 0, 1, 0, 0] -->
<dim>5</dim>
</port>
<port id="3">       <!-- pads_end value: [0, 0, 1, 0, 0] -->
<dim>5</dim>
</port>
</input>
<output>
<port id="3">
<dim>48</dim>   <!-- data.shape[0] \* block_shape.shape[0] \* block_shape.shape[1] \*... \* block_shape.shape[4] -->
<dim>3</dim>    <!-- (data.shape[1] + pads_begin[1] + pads_end[1]) / block_shape.shape[1]  -->
<dim>3</dim>    <!-- (data.shape[2] + pads_begin[2] + pads_end[2]) / block_shape.shape[2] -->
<dim>1</dim>    <!-- (data.shape[3] + pads_begin[3] + pads_end[3]) / block_shape.shape[3] -->
<dim>3</dim>    <!-- (data.shape[4] + pads_begin[4] + pads_end[4]) / block_shape.shape[4] -->
</port>
</output>
</layer>